In my personal opinion, the 300 f/2.8L IS gives you a lot of flexibility when coupled with extenders. For years, I used a 500 f/4L IS and finally gave up on it because of the weight. The 400 f/2.8L IS is even heavier than the 500. It's a brute and weighs over 6 pounds more than the 300. I am not familiar with the non-IS version, but I'm sure it's a pretty heavy lens as well. Monopod or not, you still have to carry your gear around.
I shoot mostly motorsports and birds and am amazed at how the 300 performs in those venues. The AF is incredibly fast and accurate. The image quality, simply put..... is outstanding.
Don't forget to click on the images to enlarge them.Here are some images using the lens without a converter (300mm).....



Here are some images using the 1.4x converter (420mm).....




Here are some images using the 2x converter (600mm).....




I'm using the Mark III converters and found the 2x is much better than the previous model, although did not see much difference with the 1.4x to the older model.
I normally shoot a 1D Mark IV but also use the above combos on a 7D which also handles them very well.
They will have to pry my 300 f/2.8L IS from my cold, dead hands.